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By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…
In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases…
This paper addresses two questions: (a) can we identify a sensible class of 2-parameter persistence modules on which the rank invariant is complete? (b) can we determine efficiently whether a given 2-parameter persistence module belongs to…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves…
Recommender systems often rely on graph-based filters, such as normalized item-item adjacency matrices and low-pass filters. While effective, the centralized computation of these components raises concerns about privacy, security, and the…
Topological invariants, including the Chern numbers, can topologically classify parameterized Hamiltonians. We find that topological invariants can be properly defined and calculated even if the parameter space is discrete, which is done by…
Many complex chemical problems encoded in terms of physics-based models become computationally intractable for traditional numerical approaches due to their unfavourable scaling with increasing molecular size. Tensor decomposition…
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…
This paper proposes a novel framework for delay-tolerant particle filtering that is computationally efficient and has limited memory requirements. Within this framework the informativeness of a delayed (out-of-sequence) measurement (OOSM)…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…
Deep networks are nowadays becoming popular in many computer vision and pattern recognition tasks. Among these networks, deep kernels are particularly interesting and effective, however, their computational complexity is a major issue…
Here we define a procedure for evaluating KL-projections (I- and rI-projections) of channels. These can be useful in the decomposition of mutual information between input and outputs, e.g. to quantify synergies and interactions of different…
We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can…
Fibres shed from our clothes during a washing machine cycle constitute around 35% of the primary microplastics in our oceans. Current conventional dead-end washing machine filters clog relatively quickly and require frequent cleaning. We…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…